Abstract
This paper answers a question raised by Grothendieck in 1970 on the “Grothendieck closure” of an integral linear group and proves a conjecture of the first author made in 1980. This is done by a detailed study of the congruence topology of arithmetic groups, obtaining along the way, an arithmetic analogue of a classical result of Chevalley for complex algebraic groups. As an application we also deduce a group theoretic characterization of thin subgroups of arithmetic groups.
Original language | English |
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Pages (from-to) | 1281-1298 |
Number of pages | 18 |
Journal | Algebra and Number Theory |
Volume | 13 |
Issue number | 6 |
DOIs | |
State | Published - 2019 |
Bibliographical note
Publisher Copyright:© 2019, Mathematical Sciences Publishers. All rights reserved.
Keywords
- Congruence subgroup
- Thin groups